Lecture #20, October 18, 2006  
Cruising in to Chapter 16 


Lecture Outline (some material shown is lookandlisten only)  Quantum Theory of the Chemical Bond


If destructive interference represents the orbital in which the electron happens to be found, the linear combination results in a depeletion of electron density between the positively charged protons. They repel each other under these circumstances.  
A schematic of the orbitals on separated protons relative to "close" protons. The constructive combination of atomic orbitals gives rise to a system lower in energy than the isolated system and is a bonding molecular orbital.  
Energy diagram and geometry for the sigma1s (bonding) orbital construction.  
Redefining how one calculates bond order within the context of molecular orbital theory.  
The molecular orbital energy diagram for H_{2}^{}
and other isoelectronic species, all having bond order =
0.5. The electron configuration would be written as s_{1s}^{2} s^{*}_{1s}^{2
}s_{2s}^{2} or, as in the current text, simply s_{s}^{2} s^{*}_{s}^{2 }s_{s}^{2}. 

Energy diagram and geometry for the sigma*1s (antibonding) orbital construction  
Molecular orbital energy diagrams for 1, 2, 3, and 4 electrons systems. The correspondence between bond order and bondlength and between bond order and bond energy is shown for each molecular species.  
The molecular orbital energy diagram for Li_{2} containing all six electrons. Since antibonding electrons negate the effect of bonding electrons, the pair of s* electrons cancels out the bonding characteristics of the pair of s electrons and both pairs revert to the inner core 1s^{2} configurations that we expect from simpler considerations. The electron configuration could thus be written as [He][He]s_{2s}^{2}.  
The molecular orbital energy diagram for Be_{2}. Since the number of antibonding electrons is equal to the number of bonding electrons, there is no net bonding in this molecule and it simply breaks back up into two Be atoms.  
Energy diagram and geometry for the sigma2p_{x} (bonding) orbital construction from the 2p atomic orbitals originally directed along the bonding (x) axis.  
This (with luck) is an animation of the computergenerated s_{2p} (or s_{p}) bonding molecular orbital showing how the symmetry about the bond axis resembles that for the satomic orbital's symmetry about the nucleus. Hence the s label.  
Energy diagram and geometry for the sigma*2p (antibonding) molecular orbital construction  
A reminder that, perpendicular to the bond axis in the xdirection, there are 2p atomic orbitals in the zdirection and in the ydirection. Just the 2p_{y} orbitals on each atom are shown here.  
Energy diagram and geometry for the pi2p_{y} (bonding) molecular orbital construction from the 2p atomic orbitals originally pointing in the ydirection, perpendicular to the bond axis and in the plane of the illustration. Constructive interference occurs in the region of overlap. (Recognize that there is an identical pi bonding level, same energy, constructed in the xdirection from the 2p_{z} atomic orbitals.)  
For "diboron", B_{2} we get a somewhat surprising result out of the molecular orbital energy diagram and the ensuing electron configuration. The ninth and tenth electrons go into the lowest energy available orbitals. These are the p orbitals. There are two of equal energy and Hund's rule forces us to put one electron in each and with parallel spins. Thus we have bond order = 1, a single bond, but it is not a sigma bond. In fact, there is one electron in one piorbital and another electron in a second piorbital comprising this single bond. 